Related papers: Mean Field Games and Control on Large Expander Gra…
The modelling of linear quadratic Gaussian optimal control problems on large complex networks is intractable computationally. Graphon theory provides an approach to overcome these issues by defining limit objects for infinite sequences of…
This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a new framework to prove convergence…
This paper studies a general class of stochastic population processes in which agents interact with one another over a network. Agents update their behaviors in a random and decentralized manner according to a policy that depends only on…
This article aims at quantifying the long time behavior of solutions of mean field PDE systems arising in the theory of Mean Field Games and McKean-Vlasov control. Our main contribution is to show well-posedness of the ergodic problem and…
We propose a theoretical framework for training Graph Neural Networks (GNNs) on large input graphs via training on small, fixed-size sampled subgraphs. This framework is applicable to a wide range of models, including popular sampling-based…
This paper discusses the control of coherent structures in turbulent flows, which has broad applications among complex systems in science and technology. Mean field games have been proved a powerful tool and are proposed here to control the…
In Mean Field Games of Controls, the dynamics of the single agent is influenced not only by the distribution of the agents, as in the classical theory, but also by the distribution of their optimal strategies. In this paper, we study…
In this paper, we derive the asymptotic distribution of the number of copies of a fixed graph $H$ in a random graph $G_n$ sampled from a sparse graphon model. Specifically, we provide a refined analysis that separates the contributions of…
Most networks are not static objects, but instead they change over time. This observation has sparked rigorous research on temporal graphs within the last years. In temporal graphs, we have a fixed set of nodes and the connections between…
Power grids are undergoing major changes from a few large producers to smart grids build upon renewable energies. Mathematical models for power grid dynamics have to be adapted to capture, when dynamic nodes can achieve synchronization to a…
Graphons, as limits of graph sequences, provide an operator-theoretic framework for analyzing the asymptotic behavior of graph neural operators. Spectral convergence of sampled graphs to graphons induces convergence of the corresponding…
In this paper, we exploit the theory of dense graph limits to provide a new framework to study the stability of graph partitioning methods, which we call structural consistency. Both stability under perturbation as well as asymptotic…
Secure multiparty computation (MPC) on incomplete communication networks has been studied within two primary models: (1) Where a partial network is fixed a priori, and thus corruptions can occur dependent on its structure, and (2) Where…
Mean field games are concerned with the limit of large-population stochastic differential games where the agents interact through their empirical distribution. In the classical setting, the number of players is large but fixed throughout…
In this brief note, we report a formal mathematical observation: we are about to breach a major century-old barrier in the analysis of interacting particle systems. More precisely, it is well-known that in…
Graph neural networks (GNNs) are learning architectures that rely on knowledge of the graph structure to generate meaningful representations of large-scale network data. GNN stability is thus important as in real-world scenarios there are…
This paper establishes the existence of relaxed solutions to mean field games (MFGs for short) with singular controls. We also prove approximations of solutions results for a particular class of MFGs with singular controls by solutions,…
In this paper, we propose an initial value fomulation of the discrete mean field games on finite graphs (Graph MFG), and design a neural network based approach to solve it. Graph MFG describes infinite, non-cooperative and interactive…
In this paper, we study a model for opinion dynamics where the influence weights of agents evolve in time via an equation which is coupled with the opinions' evolution. We explore the natural question of the large population limit with two…
This paper studies the convergence of mean field games with finite state space to mean field games with a continuous state space. We examine a space discretization of a diffusive dynamics, which is reminiscent of the Markov chain…